Initial applications of the \(\mathsf {MEM}\)  were favored by the fact that GARCH routines in standard software could expediently be used to estimate the new model, by imposing that the "dependent variable" were the square root of the actual variable of interest, that the mean equation was forced to zero, and that the innovation distribution was set to the Gaussian. This estimation practice was later justified in a more general context by [1]}, who formally proved the result for a Gamma distribution for the multiplicative innovation, and showed that the first order conditions for the ML estimation of the parameters of the conditional expectation in a \(\mathsf {MEM}\)  do not depend upon the unknown scale parameter of the Gamma, establishing QMLE properties for the estimator. Independently developed, the Generalized Autoregressive Score approach of [2]} and the Dynamic Conditional Score approach by [3]} both address a wider class of models which comprise the \(\mathsf {MEM}\)  as a special case under a parametric assumption of a Gamma distribution for the error term.
